There is almost no winter tyre reference that matches rear summer tyres for M135i (245/35/18).
Technically speaking there is no reason reason 225/45/18 (which is the official size for winter tyres on that car) could not fit. It is within the supported range for 8'' rims in ETRTO Standards . My dealer is telling me the same story and I requested that they explain what is the issue. So far I am still waiting for an explanation.

I guess the main point is that officially M135i is supposed to have 4 identical 7.5'' rims for winter tyres and a mix of 8'' (front) and 7.5'' (rear) with summer tyres. So more or less we are asking them to get out what is proposed by the factory. Not sure most of them are ready to do that.

It is not dangerous. In the summer, I am running 8" wheels with 205-tires!
I think BMW prefers to equip the M135i with wider tires in the rear to get more power down in the summer. In snow and slush, you get more grip by running narrower tires, so it is a bit risky to use wide rear tires in the winter. 225 all around makes sense, and it doesn't matter if the wheels are 7.5" or 8".

Because the 388 styling is delivered with wintertires 225 and also As a summerset with 245 rear?
In the advertisment of the 388 they say front is 7,5 and rear 8J

Is it possible that 388 wheels have different sizes for winter and summer?

I truly cannot find any reason but the one expressed: it is outside of what is proposed by the factory...
Afterwards taking into account they offer 388 in 7.5x18/ET45 and 8x18/ET52 they can cover all their usual expectations: 4x7.5 for a winter set and 2x7.5'' with 2x8'' for a summer set. The concern is more for us. With such mix you are ending with 6 wheels and you do not even benefit from having a specific set for each season.

The dealer offered me 1200 euro for the original set. The 388 styling summerset is 2300 euro.

If I really like the 388 winterset I'll have the same for summer

Be careful on one point while fitting 225/40/18 on 8'' rim is fine, fitting 245/35/18 on 7.5'' is not within recommended range of ETRTO. So if you expect to reuse your winter set in summer it will probably not be supported by your insurance (on contrary to use the mixed summer set with winter wheels)...

I am running 225/40/18 michelin pilot alpin a4 (non runflat) on the original wheels. They fit fine on both the 7.5j front on 8j rear.
For summer I put on the original tyres on breyton gts-r 18 inch set 7.5j front and 8.5j rear. Again these wheels accept the 225 and 245 rear without any problem.

If you want same winter set only option is the pirelli sottozero runflat. They are the only one making a 245/35/18 winter wheel.

Tyres officially supported for M135i exist with and without runflat. So there is no reason to have to get them with runflat unless you don't mind.
If you have good relationships with your dealer, I am sure he can propose for the summer set something without runflat (Michelin PSS are recommended tyres and they do not exist in runflat).
Besides that rather than saving few euros and get tyres that I dislike and will try to trash the earliest as possible, I personally prefer to get straight something that I am happy to live with. Even more for summer when "spirited driving" happens more often for me than in winter.

This is obviously a personal point of view not better or worse than another one.

Runflat is fine by me, but all I want is that I could use the 388 for summerwheels and the 436 for winterwheels. But that seems not to be possible without a 3th set of wheels,

the point is not about the runflat.

As I said earlier, the question is whether you want to stick to what you dealer wants or what is technically possible. From a technical point of view, what you want to do is possible without any problem.
However, if you want to please your dealer you buy two additional 436 rim sold for the front (7.5''x18) and use the two others you already have. You will get the 4x7.5''x18 required to please BMW sales department and still use 436 for winter.